Question: Rewrite as a simplified fraction. ${3.1\overline{4} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 314.4444...\\ 10x &= 31.4444...\end{align*}}$ Subtracting the two equations, we have: ${90x = 283}$ ${x = \dfrac{283}{90}} \text{or} {3 \dfrac{13}{90}}$